相关论文: Metaplectic tensor products for automorphic repres…

We prove that for any m > 1 given any m-tuple of Hecke eigenforms $f_i$ of level 1 whose weights satisfy the usual regularity condition there is a self-dual cuspidal automorphic form $\pi$ of $\GL_{2^m}(\Q)$ corresponding to their tensor…

In this article, we establish an asymptotic lower bound estimate on the contribution of cuspidal automorphic representations of ${\rm GL}_4(\mathbb A_{\mathbb Q})$ to cuspidal cohomology of the ${\rm GL}_4$ which are obtained from…

In this note we compute some local unramified integrals defined on metaplectic covering groups of $GL$. These local integrals which were introduced by Suzuki, represent the standard tensor product $L$ function $L(\pi^{(n)}\times…

A family of global integrals representing a product of tensor product (partial) $L$-functions: $ L^S(s,\pi\times\tau_1)L^S(s,\pi\times\tau_2)... L^S(s,\pi\times\tau_r) $ are established in this paper, where $\pi$ is an irreducible cuspidal…

We construct Rankin-Selberg integrals using Bessel models for a product of tensor product partial $L$-functions \begin{equation*} L^S(s,\pi\times\tau_1) L^S(s,\pi\times\tau_2)\cdots L^S(s,\pi\times\tau_r) \end{equation*} where $\pi$ is an…

In this paper, we explicitly determine the local $2$-adic component of a non-selfdual automorphic representation $\Pi$ of $\mathrm{GL}_3$ constructed by van Geemen and Top. We prove that $\Pi_2$ is a parabolically induced representation of…

We present an integral representation for the tensor product $L$-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. Our construction is uniform over all classical…

Let $\pi=\pi_1 \otimes \pi_2 \otimes \pi_3$ be a unitary cuspidal automorphic representation of $\mathrm{GL}_3^3(\mathbb{A}_F)$ where $F$ is a number field. Assume that $\pi$ is everywhere tempered. Under suitable local hypotheses, for a…

We prove the compatibility of local and global Langlands correspondences for $GL_n$ up to semisimplification for the Galois representations constructed by Harris-Lan-Taylor-Thorne and Scholze. More precisely, let $r_p(\pi)$ denote an…

We describe the tensor products of two irreducible linear complex representations of the finite general linear group G = GL(3,q) in terms of induced representations by linear characters of maximal torii and also in terms of Gelfand-Graev…

We study some tempered endoscopic cases of Langlands functoriality on the $n$-variable unitary groups via the simple stable trace formula. This extends previous work of Rogawski and Clozel-Harris-Labesse. Ramakrishnan and Kim-Shahidi have…

We define a tensor product of linear sites, and a resulting tensor product of Grothendieck categories based upon their representations as categories of linear sheaves. We show that our tensor product is a special case of the tensor product…

In the first part of the book, we classify the automorphic representations of {\rm GSp}(2) which are invariant under tensor product with a given quadratic id\`ele class character, via the lifting of automorphic representations of twisted…

We consider a new integral representation for $L(s_1, \Pi \times \tau_1) L(s_2, \Pi \times \tau_2),$ where $\Pi$ is a globally generic cuspidal representation of $GSp_4,$ and $\tau_1$ and $\tau_2$ are two cuspidal representations of $GL_2$…

In this paper, we study the order of the pole of the triple tensor product $L$-functions $L(s,\pi_1\times\pi_2\times\pi_3,\otimes^3)$ for cuspidal automorphic representations $\pi_i$ of $\mathrm{GL}_{n_i}(\mathbb{A}_F)$ in the setting where…

We introduce a new topological coproduct $\Delta^{\psi}_{u}$ for quantum toroidal algebras $U_{q}(\mathfrak{g}_{\mathrm{tor}})$ in all untwisted types, leading to a well-defined tensor product on the category…

Let $\pi_1, \pi_2, \pi_3$ be three cuspidal automorphic representations for the group ${\rm SL}(2, \Bbb{Z})$, where $\pi_1$ and $\pi_2$ are fixed and $\pi_3$ has large conductor. We prove a subconvex bound for $L(1/2, \pi_1 \otimes \pi_2…

Let $ G $ be a connected semisimple Lie group with finite center. We prove a formula for the inner product of two cuspidal automorphic forms on $ G $ that are given by Poincar\'e series of $ K $-finite matrix coefficients of an integrable…

In this paper we establish a new case of Langlands functoriality. More precisely, we prove that the tensor product of the compatible system of Galois representations attached to a level-1 classical modular form and the compatible system…

Let $\pi$ be a cuspidal automorphic representation of $GL_n(\mathbb{A}_\mathbb{Q})$ which satisfies certain reasonable assumptions such as integrality of Hecke polynomials, the existence of mod $\ell$ Galois representations attached to…